If \(-\Delta \)  is an eigenvalue then \(G\)  is bipartite and therefore has symmetric spectra. If \(G\)  has exactly 2 eigenvalues then \(G\)  is complete and bipartite (So \(G=K_2\) ). If \(G\)  has exactly 4 eigenvalues then \(G\)  is a regular bipartite graph with exactly 4 eigenvalues and must therefore be the incidence graph of a symmetric \(2-(v,k,\lambda )\)  design, as shown in [1]}.
